Advertisements
Advertisements
प्रश्न
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`(x + 1)^2/100 + (y - 2)^2/64` = 1
Advertisements
उत्तर
It is an ellipse.
The major axis is parallel to the x-axis.
a2 = 100, b2 = 64
a = 10, b = 8
c2 = a2 – b2
= 100 – 64 = 36
c = 6
ae = 6
10e = 6
e = `6/10 = 3/5`
Centre (h, k) = (– 1, 2)
Vertices (h ± a, k) = (– 1 ± 10, 2)
= (– 1 + 10, 2) and (– 1 – 10, 2)
= (9, 2) and (– 11, 2)
Foci (h ± c, k) = (– 1 ± 6, 2)
= (– 1 + 6, 2) and (– 1 – 6, 2)
= (5, 2) and (– 7, 2)
Directrix x = `+- "a"/"e" + "h"`
= `+- 10/(3/5) - 1`
= `+- 50/3 - 1`
x = `50/3 - 1` and x = `50/(-3) - 1`
= `47/3` and `(- 53)/5`
APPEARS IN
संबंधित प्रश्न
Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola
x2 = - 16y
The profit ₹ y accumulated in thousand in x months is given by y = -x2 + 10x – 15. Find the best time to end the project.
Find the equation of the parabola which is symmetrical about x-axis and passing through (–2, –3).
Find the axis, vertex, focus, equation of directrix and the length of latus rectum of the parabola (y - 2)2 = 4(x - 1)
Find the equation of the parabola in the cases given below:
Focus (4, 0) and directrix x = – 4
Find the equation of the parabola in the cases given below:
Vertex (1, – 2) and Focus (4, – 2)
Find the equation of the ellipse in the cases given below:
Foci `(+- 3, 0), "e"+ 1/2`
Find the equation of the ellipse in the cases given below:
Length of latus rectum 4, distance between foci `4sqrt(2)`, centre (0, 0) and major axis as y-axis
Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
y2 = – 8x
Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
y2 – 4y – 8x + 12 = 0
Prove that the length of the latus rectum of the hyperbola `x^2/"a"^2 - y^2/"b"^2` = 1 is `(2"b"^2)/"a"`
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`(x - 3)^2/225 + (y - 4)^2/289` = 1
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`(y - 2)^3/25 + (x + 1)^2/16` = 1
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
9x2 – y2 – 36x – 6y + 18 = 0
The latus-rectum of a conic section is:
The fixed straight line used in the definition of a conic section is called the:
If the eccentricity e > 1, the conic section is:
